## Numerical solution of singularly perturbed delay differential equations with layer behavior.(English)Zbl 1474.65192

Summary: We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into $$k$$ subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree $$n$$ and determined Bezier curves on any subinterval by $$n + 1$$ control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.

### MSC:

 65L03 Numerical methods for functional-differential equations 34K10 Boundary value problems for functional-differential equations 65L11 Numerical solution of singularly perturbed problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations
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